Results on qualitative features of periodic solutions of KdV

T. Kappeler; B. Schaad; P. Topalov

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-7
  • ISSN: 2266-0607

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Kappeler, T., Schaad, B., and Topalov, P.. "Results on qualitative features of periodic solutions of KdV." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-7. <http://eudml.org/doc/251176>.

@article{Kappeler2011-2012,
author = {Kappeler, T., Schaad, B., Topalov, P.},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {eng},
pages = {1-7},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Results on qualitative features of periodic solutions of KdV},
url = {http://eudml.org/doc/251176},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Kappeler, T.
AU - Schaad, B.
AU - Topalov, P.
TI - Results on qualitative features of periodic solutions of KdV
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 7
LA - eng
UR - http://eudml.org/doc/251176
ER -

References

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  2. B. Grébert, T. Kappeler, J. Pöschel: Normal form theory of the NLS equation, preliminary version, arxiv.org/abs/0907.3938v1 2009. To appear in EMS Series of Lectures in Mathematics, EMS Publishing House. 
  3. A. Its, V. Matveev : A class of solutions of the Korteweg-de Vries equation(in Russian), Problems in Math. Physics N08, Izdat. Leningrad Univ., Leningrad, 1976 , 79-92. MR516298
  4. T. Kappeler: Fibration of the phase-space for the Korteweg-de Vries equation, Ann. Inst. Fourier 41 (1991), 539-575. Zbl0731.58033MR1136595
  5. T. Kappeler, M. Makarov: On action-angle variables for the second Poisson bracket, Comm. in Math. Phys., 214, 3 (2000), 651-677. Zbl1003.37038MR1800865
  6. T. Kappeler, M. Makarov: On Birkhoff coordinates for KdV, Ann. H. Poincaré 2 (2001), 807 - 856. Zbl1017.76015MR1869523
  7. T. Kappeler, J. Pöschel: KdV & KAM, Ergebnisse Math. u. Grenzgebiete, Springer, Berlin, 2003. MR1997070
  8. T. Kappeler, B. Schaad, P. Topalov: mKdV and its Birkhoff coordinates, Physica D: Nonlinear Phenomena, 237, 10-12 (2008), 1655-1662. Zbl1143.76400MR2454610
  9. T. Kappeler, B. Schaad, P. Topalov: Asymptotic estimates of spectral quantities of Schrödinger operators, arXiv: 1107.4542. Zbl1317.81119
  10. T. Kappeler, B. Schaad, P. Topalov: Qualitative features of periodic solutions of KdV, arXiv: 1110.0455. Zbl1274.35330
  11. T. Kappeler, P. Topalov: Global fold structure of the Miura map on L 2 ( 𝕋 , ℝ ) , Int. Math. Research Notices (2004), 2039-2068. Zbl1076.35111MR2062735
  12. T. Kappeler, P. Topalov: Global wellposedness of KdV in H - 1 ( 𝕋 , ℝ ) , Duke Math. J. 135 (2006), 327-360. Zbl1106.35081MR2267286
  13. S. Kuksin: Damped driven KdV and effective equation for long-time behaviour of its solution, preliminary version, 2009. MR2738999
  14. S. Kuksin, G. Perelman: Vey theorem in infinite dimensions and its application to KdV, Discrete and Continuous Dynamical Systems Ser. A, 27, no 1, (2010), 1-24. Zbl1193.37076MR2600759
  15. S. Kuksin, A. Piatnitski: Khasminskii - Whitham averaging for randomly perturbated KdV equation, J. Math. Pures Appl. 89 (2008), 400-428. Zbl1148.35077MR2401144
  16. V. Marchenko: Sturm-Liouville operators and applications, Birkhäuser, Basel, 1986. Zbl0592.34011MR897106
  17. H. McKean, E. Vaninsky: Action-angle variables for the cubic Schroedinger equation, Comm. Pure Appl. Math. 50 (1997), 489-562. Zbl0990.35047MR1441912
  18. A. Savchuk, A. Shkalikov: On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces, Math. Notes 80, no 6 (2006), 864-884. Zbl1129.34055MR2311614
  19. B. Schaad: Qualitative features of periodic solutions of KdV, PhD thesis, University of Zurich, 2011. Zbl1274.35330

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